Does structural linguistics still have relevance today?

The Wikipedia entry is both right and wrong on this account. Here are some perspectives.

1. Few linguists would call themselves structuralists, today (although some still would admit that heritage when asked).
2. Structuralism was an explicit theoretical framework (most cogently expressed by the Prague Circle in their Theses from 1929) in its most productive phase but for many it descended into a few random prescriptions.
3. Saussure does not represent the entirety of structuralism. He is indeed probably wrong on most things, however, he still represents a good starting point to introducing people to the study of language and I find Mark Turner's comment very injudicious.
4. Structural analysis of language is still the go to method for most language researchers even if they don't subscribe to the theoretical assumptions behind it. Indeed, Chomsky has been rightly called a structuralist (by Frederick Newmeyer) even if he started out in opposition to the structuralist establishment of his day.
5. Many of Saussure's views are simply assumed by many modern linguists but it is important to understand they were formulated for the purpose of introductory lectures and published by his students from their notes.
6. Many linguists would benefit greatly from engaging with many structuralist classics more deeply. I'd recommend Jakobson, Hjelmslev, even Saussure's course, itself. Definitely read the Prague Circle Theses. I found some of the most starkly formulated ideas about structuralism in Mukarovsky (although I'm not sure about the translation status). Of course, probably the most accessible (both in terms of language and ease of obtaining the text) would be Bloomfield's language, a founding text of American descriptivism. Combining it with Sapir's language will give you a pretty solid idea of how actual structuralists thought about language. [Although neither was an out and out structuralist, you can easily read them side by side with people from Prague, Copenhagen or Paris and see huge affinities.]
7. Not only is structuralism still alive in much of modern analytic work, so is its precursor, Russian formalism. You could do a lot worse than read Propp's Morphology of the Fairytale.
8. It is true that much of the structuralist agenda got mangled by incautious non-empiricist applications in other disciplines such as literary theory or philosophy. But I'd still recommend that good structuralist literary analysis is probably the best place to start.
9. My tentative personal recommendation would be to start all undergrad students of linguistics on a dose of structuralism and slowly dismantle it over the course of their study. I find that going in the opposite direction does not necessarily work, as well.

PS: For those who read Czech, I wrote at some lengths about the Prague School and Cognitive Linguistics in the afterword to my translation of Lakoff's Women, Fire, and Dangerous Things. Full text here: http://cogling.info/node/30. My conclusion: There are many important connections in the idea of functional motivation of linguistic structures but when pressed Prague linguistics returned to formal analyses and never developed a cognitively realistic semantics.